Famous British lingerie firm Rigby & Peller, whose clients include the Queen as well as Hollywood royalty such as Scarlett Johansson, has been snapped up by one its suppliers.

The family-run firm, which is as famous for its rigorous bra fitting service as its discretion, has sold an 87% stake to Belgian bra-maker Van de Velde for £8m.

The deal delivers a substantial windfall for the Kenton family who have retained a minority stake. Husband and wife team June and Harold Kenton bought the business in 1982 for £20,000 and latterly their children, Jill and David, have helped to run the business.

June Kenton, who after more than 50 years in the brassiere business says she can judge a woman's bust size just by looking at her, said it was the right time to sell as the company needed a partner to fulfil its ambitions for growth. However, both she and her son will continue to have a say in its future: "It will be business as usual," said the 75 year-old, adding: "When we open new stores I'll be running around doing fittings, I'll be flying all over the world for them."

Ignace van Dooselare, Van de Velde's chief executive, said: "It is our intention to work closely with both the Kenton family and the existing management team, to invest and grow Rigby & Peller both in the UK and internationally."

Part of Rigby & Peller's cachet stems from its royal warrant. Kenton has been making trips to Buckingham palace for more than 50 years in her official capacity as "corsetieres to HM Queen Elizabeth" and during her long career has served several generations including the Queen, the Queen Mother, Princess Margaret and even Princesses Beatrice and Eugenie. It was even the fitter for the Two Ronnies' costume extravaganzas in the 70s and 80s, but in recent years the firm has also won over pop royalty with Lady Gaga wearing its underwear as outerwear.

The company was founded in 1939 from a single shop on London's South Molton Street by two corsetieres: Gita Peller, a Jewish refugee who fled Hungary (legend has it with corsetry samples in her suitcase) and Bertha Rigby, who took her in when she arrived in Britain.

Today Rigby & Peller's bras sell for between £50 and £100 although a bespoke one can cost up to £200. It has seven stores and had annual sales of £10.1m in 2010. Last year Van de Velde, which designs and manufactures lingerie and is listed on the Brussels stock exchange, enjoyed sales of €166.3m (£145m).

Kenton said that the two companies had been working together for a long time and the family finally agreed to a deal as Van de Velde shared its "values and vision" and made "the most amazing bras". Before the deal Rigby & Peller was the Belgian group's biggest British stockist selling its Prima Donna and Marie Jo brands.

"Our staff and customers rely on us to deliver high standards in product and service," said Kenton. "Like us, [Van de Velde] are a family-oriented company and appreciate the value of heritage while looking to the future for growth and success."